Jeff, Gary R., List: As I have mentioned before, my university class on modern physics was more than three decades ago, so I am not fully up to speed on more recent developments in the "standard model" of *scientific* cosmology. With that disclaimer, Jeff's exposition strikes me as very much on the mark, including the prospect of drawing insights from Peirce's *metaphysical *cosmology (Gary's #1 below) with the goal of addressing--and, in a best-case scenario, resolving--the well-established inconsistencies between general relativity and quantum mechanics under the "big bang" theory, which is the current consensus.
Most notably, Jeff has put his finger on the fundamental presupposition underlying modern scientific explanations of events that purportedly occurred in the very distant past--that natural laws and processes have (more or less) *always *operated in exactly the same way that we observe them operating today. Peirce rejected that untestable assumption, instead suggesting the alternative hypothesis "that all laws are results of evolution; that underlying all other laws is the only tendency which can grow by its own virtue, the tendency of all things to take habits" (CP 6.101, 1902). JBD: Instead of supposing the cosmos was initially very small and then, in a “Big Bang” dramatically inflated in a very short amount of time, I'd like to explore the hypothesis that the timeframe and size of the universe was, in the very, very early period, indeterminate. This is exactly what Peirce advocated. "That first moment of time was of course infinitely long ago. But more than that, although it was but one moment, it was infinitely longer than any number of ages. It contained as great a multitude of ages as there are points upon a continuous line. In one sense this continuum was not time, it is true, because it all occupied but a moment of time. But it was not only strictly analogous to time, but it gradually and continuously developed into time; so that it was of one continuous nature with time" (NEM 4:139, 1897-8). "I am inclined to think ... that past time had no definite beginning, yet came about by a process which in a generalized sense, of which we cannot easily get much idea, was a development" (CP 6.505, c. 1906). JBD: 1ns - Pure Potentiality as Quality: The primordial condition is a field of highly vague, undifferentiated potential having a continuum of qualities, comparable to a pre-metric manifold. Again, the initial presence of "a continuum of qualities" entails primordial 3ns, not just 1ns; especially in conjunction with the fact that 2ns cannot be *built up* from 1ns, and 3ns cannot be *built up* from 1ns and 2ns (Gary's #2-3 below). Any *individual *quality in itself is 1ns, any quality that is actually *embodied* in something is 2ns, and any general *spectrum *of potential qualities is 3ns; for example, between any two shades of red, there are inexhaustibly many intermediate shades. "That which is possible is in so far *general *and, as general, it ceases to be individual ... the word 'potential' means *indeterminate yet capable of determination in any special case*" (CP 6.185, 1898). For the record, such an understanding is not at all unique to Gary and me; for example, Nicholas Guardiano ably presents it in a 2015 paper ( https://www.academia.edu/28270096/The_Categorial_Logic_of_Peirces_Metaphysical_Cosmogony). As he summarizes, "First, there is the ultimate origin of the universe that consists in a master continuum of the most abstract kind of potentiality. [3ns] ... The second stage, following from the first, Peirce calls the 'Platonic world.' [1ns] ... The next and third stage is the actual world in which we reside [2ns]" (p. 316). JBD: How might we move from informal diagrams and toy models (e.g. a spot of ink on a page, a blackboard, rolling of dice, drawing from an urn, etc.) to formal models? What mathematical frameworks should we draw on for the sake of developing models that will enable us to make the hypotheses about the law of mind and the growth of order more exact? I do not have answers to these questions, but they seem like the right ones to be asking. I commend Jeff for tackling them, along with any others who possess the necessary knowledge and tools to do so with appropriate rigor. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Mon, Oct 6, 2025 at 11:54 PM Gary Richmond <[email protected]> wrote: > List, > > Before we plunge (hopefully) into exploring Peircean cosmology in relation > to contemporary cosmological views (and vice versa), I would like to make th > ree general remarks about Peirce's late cosmology which, whatever yet is > unresolved in our different views (although his most recent post answers > the most important questions I've put to him), I believe both Jon and I > agree upon the following points, principally because they come with > *considerable > textual support*. > > 1. Peirce's cosmology does *not* concern the fundamental laws of physics. > Rather, he is offering a hypothesis as to how those very laws came about in > the first place. That is metaphysics, not physics. As I earlier noted, Jeff > has already pointed to this *essential *point near the end of his post > introducing this thread. > > 2. Peirce explicitly makes clear that 3ns does *not *result from 1ns and > 2ns. In fact he argues that this is* impossible*, that 3ns cannot be > built up from 1ns and 2ns. Quotations to that effect have been > repeatedly offered on the List. Rather, as has been noted here (again, > repeatedly for decades), 3ns *involves* 2ns and 1ns. Peirce's category > theory is (*wherever* it may be applied including, of course, to > metaphysics) top-down, not bottom-up. > > 3. Peirce makes clear that continuity is "original" and "inherent in > potentiality" (his words), i.e., generality (3ns) precedes both possibility > (1ns) and actuality (2ns) -- cf. 2. above. Again, many quotations have been > offered in support of this principle. > > I would also encourage those interested in Peirce's late cosmology to read > the concluding lecture in the *Cambridge Conference Lectures* of 1898 > published in paperback as* Reasoning and the Logic of Things. *The > blackboard diagram discussion begins on the bottom of page 261 (I don't > believe an online version of this lecture is available). > > In my view, nowhere is Peirce's extraordinary creative genius revealed > more fully than in this lecture series, and especially the concluding > lecture wherein I see him anticipating any number of 20th century > scientific advances. > > Best, > > Gary R > > On Mon, Oct 6, 2025 at 4:25 PM Gary Richmond <[email protected]> > wrote: > >> Jeff, List, >> >> It will take me some time to mentally assimilate your post, but it is >> most impressive, and I believe that it contributes mightily to the >> discussion of cosmology we've been having. I sincerely hope that everyone >> here interested in Peirce's cosmology in relation to contemporary versions >> reads it closely and critically. >> >> One thing I will say for now is it is helpful that you make the >> distinction between Peirce's *metaphysics* and the *physics* of current >> cosmological models. >> >> Best, >> >> Gary R >> >> On Mon, Oct 6, 2025 at 2:21 PM Jeffrey Brian Downard < >> [email protected]> wrote: >> >>> List, >>> >>> I am interested in exploring the various ways Peirce might offer >>> fruitful strategies for framing questions and hypotheses about the >>> evolution of the cosmos. Given the shift in focus from interpreting Peirce >>> to developing the ideas in the context of contemporary lines of inquiry, I >>> have given a new name for this thread. Here is a short overview of how the >>> issues might be framed: >>> >>> I. What the Competing Hypotheses Seek to Explain >>> The first second of cosmic history is the most intensively modeled and >>> least directly observed interval in all of physics. Every cosmological >>> hypothesis—standard or alternative—attempts to answer the same deep >>> question: how did stable, law-governed order emerge from the primal >>> condition of the early universe? >>> Empirically, we can observe the cosmic microwave background and infer >>> conditions back to roughly 10⁻³⁶ s after the putative “beginning.” But >>> beyond that frontier, our equations lose coherence. When we attempt to wind >>> the clock backward, general relativity (GR) predicts an initial >>> singularity—an infinitesimal point of infinite density—while quantum >>> mechanics (QM) insists that such a point cannot exist, because uncertainty >>> forbids precise localization of both energy and position. The result is a >>> conceptual fissure at the very threshold of time. >>> The challenge is twofold. First, to reconcile the gravitational >>> curvature of spacetime (the language of GR) with the probabilistic field >>> dynamics of quantum theory (the language of QM). Second, to explain the >>> apparent emergence of regularities—space, time, fields, and forces from the >>> initial conditions—whatever those are presumed to be. >>> The standard cosmological model assumes a hot, dense quantum vacuum that >>> undergoes rapid inflation, cooling into particles, forces, and atomic >>> matter through a series of symmetry-breaking transitions. Our family of >>> hypotheses, following C. S. Peirce’s metaphysical principle of >>> “habit-taking,” interprets these same transitions not as the enforcement of >>> pre-existing laws but as the evolutionary crystallization of *habits*—stable >>> relational patterns that become laws through repetition and >>> self-reinforcement. The contrast, therefore, is not merely physical but >>> ontological: one treats laws as *given*, the other as *grown*. >>> My general strategy is to question the assumption that so much happened, >>> so fast, from what was initially a very small space. Instead of supposing >>> the cosmos was initially very small and then, in a “Big Bang” dramatically >>> inflated in a very short amount of time, I'd like to explore the hypothesis >>> that the timeframe and size of the universe was, in the very, very early >>> period, indeterminate. >>> II. The Standard Cosmological Account of the Very, Very Early Universe: >>> The Six Early Epochs within the First Second >>> >>> 1. Planck Era (0 – 10⁻⁴³ s) >>> Physics as we know it breaks down. The universe’s density exceeds >>> 10⁹⁴ g cm⁻³ and the temperature surpasses 10³² K. GR predicts a curvature >>> singularity, but quantum gravitational effects should dominate. No >>> consistent theory yet unites them. >>> 2. Grand-Unification Era (10⁻⁴³ – 10⁻³⁶ s) >>> Gravity decouples from the other fundamental interactions. The >>> strong, weak, and electromagnetic forces remain unified under speculative >>> grand-unified theories (GUTs). Vacuum fluctuations drive exponential >>> inflation. >>> 3. Inflationary Epoch (≈10⁻³⁶ – 10⁻³² s) >>> The universe expands by a factor of ~10⁵⁰ in a tiny fraction of a >>> second, smoothing out inhomogeneities. Quantum fluctuations are stretched >>> to cosmic scales, seeding later galaxy formation. When inflation ends, >>> latent vacuum energy converts into matter and radiation—a process called >>> “reheating.” >>> 4. Electroweak Epoch (10⁻¹² – 10⁻⁶ s) >>> The strong force separates from the electroweak. The Higgs field >>> acquires a nonzero vacuum expectation value, giving mass to particles. W >>> and Z bosons and leptons acquire distinct identities. >>> 5. Quark Epoch (10⁻⁶ – 10⁻⁴ s) >>> The universe is a hot plasma of quarks, antiquarks, and gluons. As >>> it cools below ~10¹² K, quarks begin to bind into hadrons (protons and >>> neutrons). >>> 6. Hadron and Lepton Epochs (10⁻⁴ – 1 s) >>> Matter–antimatter annihilation occurs, leaving a slight excess of >>> baryons. Neutrinos decouple. By ~1 s, the universe is filled with >>> photons, >>> neutrinos, electrons, protons, and neutrons in near-thermal equilibrium. >>> >>> 2. The Theoretical Foundations >>> The standard model of cosmology (ΛCDM + inflation) joins: >>> >>> - General Relativity, governing the dynamics of spacetime and cosmic >>> expansion (via Einstein’s field equations). >>> - The Standard Model of Particle Physics, governing matter and >>> fields via quantum gauge theories. >>> >>> Each works remarkably well in its proper domain. GR predicts large-scale >>> structure and gravitational lensing; quantum field theory predicts particle >>> behaviors confirmed to 1 part in 10¹¹. Yet their conceptual languages >>> conflict. >>> 3. The Central Tension: GR vs QM >>> >>> - Background independence vs. fixed background: >>> GR treats spacetime geometry as dynamic; quantum theory presupposes >>> a fixed spacetime background. >>> - Deterministic vs. probabilistic law: >>> GR evolves smoothly and deterministically; quantum evolution is >>> probabilistic and discontinuous upon measurement. >>> - Continuum vs. discreteness: >>> GR’s continuum manifolds clash with QM’s quantized fields and >>> operators. >>> >>> Attempting to merge them yields contradictions. Quantizing gravity by >>> standard techniques leads to non-renormalizable infinities. String theory >>> replaces point particles with one-dimensional objects to tame those >>> divergences, while loop quantum gravity discretizes space itself into spin >>> networks. Both remain mathematically elegant yet empirically unconfirmed. >>> The deeper problem is conceptual: both assume laws are fixed and >>> pre-existent. Time, in both frameworks, is treated as a parameter that >>> orders events, not as something that itself *evolves*. When we >>> extrapolate back to t → 0, these assumptions collapse. The singularity is >>> not a physical object but a signal that the framework itself has reached >>> its limit. >>> Thus, the standard model offers a magnificent but incomplete chronicle. >>> It describes *how* the cosmos evolves from 10⁻³⁶ s onward, but not *why* >>> laws themselves appear, why symmetries break as they do, or why certain >>> constants take the values that make structure possible. >>> III. The Peircean Family of Hypotheses >>> 1. Philosophical Premise: Law as Evolving Habit >>> C. S. Peirce proposed in his 1891 essay “The Architecture of Theories” >>> that “the only possible way of accounting for the laws of nature and for >>> uniformity in general is to suppose them results of evolution.” The >>> universe, on this view, begins not in order but in pure spontaneity, a >>> chaos of ungoverned possibilities. Through repetition and reinforcement of >>> relations that persist, habits form; habits stabilize into laws. >>> 2. Ontological Ingredients: >>> >>> 1. Firstness — Pure Potentiality as Quality: The primordial >>> condition is a field of highly vague, undifferentiated potential having a >>> continuum of qualities, comparable to a pre-metric manifold. Temporal >>> relations are not well ordered. Spatial relations have very high degrees >>> of >>> freedom, approximating an infinitude of vague topological dimensions. >>> 2. Secondness — Reaction: Initially, there are no actual objects >>> having a substantial character of individuals that perdue over time. >>> Rather, highly random encounters among continuous potentials yield >>> constraints—proto-events analogous to quantum fluctuations. >>> 3. Thirdness — Mediation/Habit: Stable patterns emerge that mediate >>> between possibilities and facts; these are the early ordered habits that >>> evolve into laws having symmetries. >>> >>> This triadic cycle repeats iteratively, giving rise to more complex, >>> self-referential systems of law. Order grows as natural habits. In time, >>> these natural habits take the character of natural laws having nested >>> levels of necessity and contingency, woven together into an evolving system >>> of regularities. >>> 3. Cosmological Reformulation >>> In mathematical terms, the Peircean hypothesis treats the evolution of >>> order as a process of constraint accumulation in an initially unconstrained >>> relational manifold. Instead of assuming pre-existing spacetime, we posit >>> networks of relations—logical and topological—whose persistent interactions >>> generate the effective metric structure. >>> >>> - Temporal Order: Time is not a fixed metrical parameter but an >>> emergent order parameter expressing the persistence of relation. >>> - Metric Emergence: As habits of relation stabilize, equivalence >>> classes of relational paths become metrically consistent; curvature >>> arises >>> from deviations in those habits. >>> - Quantum Indeterminacy: Rather than randomness being primitive, >>> indeterminacy reflects ongoing openness of the habit-formation >>> process—what >>> Peirce called *tychism*. >>> >>> 4. Physical Analogues >>> In practice, these ideas correspond to several contemporary research >>> directions. Here are a few: >>> >>> - Causal-set theory, which builds spacetime from ordered relations. >>> - Process physics (Cahill, Kauffman), in which information networks >>> self-organize into geometry. >>> - Relational quantum mechanics, treating states as relations rather >>> than substances. >>> >>> The models I am developing seek to formalize these insights through >>> iterative mapping functions on networks of relations—analogous to >>> topological and projective transformations that, through self-consistency >>> constraints, converge toward a stable metric manifold. >>> 5. Epochal Reconstruction >>> In this framework, the first “second” is not a moment after a >>> singularity but a phase transition from ungoverned potential to emergent >>> order: >>> >>> 1. Pre-habit phase (Peircean Firstness): Random relation fields >>> without duration or extent. >>> 2. Formation of stable triads (Secondness → Thirdness): >>> Self-consistent relational loops persist; these become the seeds of >>> temporal and spatial continuity. >>> 3. Emergent metrics: Statistical regularities among triads define >>> curvature; gravitational attraction is a large-scale manifestation of >>> this >>> tendency of relations to cohere. >>> 4. Law consolidation: Repeated patterns establish stable >>> transformation rules—analogues of conservation laws and field equations. >>> >>> Thus, what the standard model describes as inflation and symmetry >>> breaking are interpreted as episodes of accelerated habit formation, in >>> which local relational networks reach new equilibria. >>> 6. Testable and Mathematical Implications >>> >>> - Variable constants: If laws evolve, coupling constants may vary >>> slowly over cosmic time—a testable prediction. >>> - Self-organizing field equations: Einstein’s equations appear as >>> late-stage equilibria of evolving relational space/time constraints that >>> co-evolve with the natural habits that evolve into the laws governing >>> strong, weak, and EM forces. >>> - No initial singularity: The vague highly random potential fields >>> in which space and time are not yet ordered are posited as kind of >>> limiting >>> case from which order grows as a self-limiting process. >>> >>> This metaphysical framework can be made exact by representing evolving >>> relational networks through categorical or topological formalisms, such as >>> spin networks or iterative projective geometries, providing a unified >>> schema that naturally bridges quantum discreteness and gravitational >>> continuity. >>> IV. Comparative Evaluation >>> The standard cosmological model stands as one of the great triumphs of >>> modern science. It quantitatively predicts nucleosynthesis, cosmic >>> microwave background anisotropies, and large-scale structure. Its weakness >>> lies not in what it explains, but in what it must assume: fixed laws, fixed >>> constants, and a spacetime framework that pre-exists the very universe it >>> describes. It is operationally powerful yet ontologically incomplete. When >>> traced back to the first instants, its equations give rise to tensions >>> bordering on contradictions--singularities and unexplained initial >>> conditions. >>> The Peircean family of hypotheses inverts the order of explanation. It >>> begins with chaos, not law; with relation, not substance; with habit >>> formation, not imposed rule. Its strength is conceptual coherence across >>> scales: the same logic of iterative habit formation that explains the >>> emergence of atomic stability or biological order also accounts for cosmic >>> law. It offers a genuinely evolutionary metaphysics of law, potentially >>> unifying physical and logical modes of order. >>> Yet it faces formidable challenges. It lacks a single, empirically >>> confirmed mathematical formalism equivalent to GR or quantum field theory. >>> Its language of “habits” and “relations” must be rigorously specified to >>> make testable predictions. It risks drifting toward philosophical >>> generality if not anchored in quantitative models. >>> In sum: >>> *Criterion* >>> *Standard Model* >>> *Peircean Habit Hypothesis* >>> Predictive Power >>> High (CMB, nucleosynthesis, structure) >>> Moderate (conceptual; testable via variable constants) >>> Ontological Coherence >>> Fragmented (QM vs GR) >>> Unified (laws evolve from habits) >>> Empirical Confirmation >>> Extensive >>> Emerging / indirect >>> Explanatory Depth >>> Assumes laws >>> Explains laws >>> Mathematical Formalism >>> Mature >>> Developing (categorical/topological) >>> >>> For those who, like me, would like to develop and apply Peirce's methods >>> and explanatory strategies to contemporary questions in cosmology, our work >>> is cut out for us. How might we move from informal diagrams and toy models >>> (e.g. a spot of ink on a page, a blackboard, rolling of dice, drawing from >>> an urn, etc.) to formal models? What mathematical frameworks should we draw >>> on for the sake of developing models that will enable us to make the >>> hypotheses about the law of mind and the growth of order more exact? >>> >>> Yours, >>> >>> Jeff >>> >>
_ _ _ _ _ _ _ _ _ _ ► PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] . ► <a href="mailto:[email protected]";>UNSUBSCRIBE FROM PEIRCE-L</a> . But, if your subscribed email account is not your default email account, then go to https://list.iu.edu/sympa/signoff/peirce-l . ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and co-managed by him and Ben Udell.
